Why is there a drop in residential solar installation in Seattle from 2016? The study area is Seattle and the unit of analysis is census track.

There are two noticable groups in social characteristics with solar potential (MWh): A group of high income, single family housing owners and a group of low income, multifamily housing renters. These two groups have comparatively higher potential for solar electricity generation.

Variables are collected through several datasets including National Renewable Energy Laboratory (NREL) REPLICA 2018, American Community Survey (ACS) 2011 - 2015, the Department of Housing and Urban Development (HUD) 2017 and City of Seattle open data portal.

The number of solar installation per census track is the dependant variable (sol_instl). Rest of variables are as follows.

• hu_own: a proportion of owner-occupied housing unit
• hu_blt1970: a proportion of housing units bulit before 1970
• hu_no_mor: a proportion of housing units without morgage
• hu_med_val: housing unit median value
• hu_ex_1000: total number of owner-occupied units with housing costs greater than $1000/month
• edu: a proportion of over 25 year old population with college degree and above
• wh_race: a proportion of caucasian population
• hh_med_income: household median income
• hh_gini_index: household GINI Index of income inequality
• lihtc: low income tax credit qualification (T/F)
  
• hh_high_sf_own: a proportion of households of high income, single family housing owner
• hu_mwh: solar elergy potential (MWh) per housing unit in a census track

The dependant variable (sol_instl) is correlated to all the variables except for the household GINI index and LITHC qualification.

By exploratory regression analyses, the best model with the highest R-squared (0.61) and lowest AIC (653.69) was chosen with the two variables, hu_med_val and hu_ex_1000 through OLS.

## 
## Call:
## lm(formula = sol_instl ~ hu_med_val + hu_ex_1000, data = regrs[-c(1)])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.4964 -1.8188 -0.4623  1.1230 16.2559 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.984e+00  8.119e-01  -2.444   0.0159 *  
## hu_med_val   3.905e-06  1.954e-06   1.998   0.0478 *  
## hu_ex_1000   1.768e+01  1.594e+00  11.094   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.875 on 128 degrees of freedom
## Multiple R-squared:  0.6136, Adjusted R-squared:  0.6076 
## F-statistic: 101.6 on 2 and 128 DF,  p-value: < 2.2e-16

The residual plot shows it is biased and clustered indicating the model is not catching well the variability of the dependant variable.

OLS residual mapping

Another method named Geographically Weighted Regression (GWR) was performed with the outcomes of R-squared (0.76) and AIC (625.54), which are better than the previous OLS model. Residual map shows random pattern as confirmed by auto correlation analysis with Moran's index of 0.028 and z-score of 0.75.

Residual mapping for GWR

This model tells that housing unit median value affects residential solar installation more in the area of darker red as below. These areas are more senstive to the housing unit median value with respect to the residential solar installation.

Impact of housing median value

For the variable, total number of owner-occupied units with housing costs greater than $1000/month, the more sensitive area is presented as darker red in the map below.

impact of housing cost over $1k/ month

Each point represents the house unit with residential solar system installed on its building since 2003. By aggregating these points to the census track, hotspot areas and outliers were identified as below.

Solar installation hotspot

Solar installation outlier

It would be useful to include all the variables rather than selecting only two variables in the model. With a factor analysis, all the variables would be used for model identification. The parallel screen confirms 2 or 3 factors would be appropriate.

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA

The 3 factos partially explain each variable depending on the latent characteristics.

The first factor (ML1) is more related to the higher housing stability, the 2nd factor (ML2) to the higher economic status, and the 3rd factor (ML3) is more related to the higher income inequality.

The most loaded, ML1 is positively correlated with the solar installation variable.

## [1] 131   3

The value of R-squared of the factor regression is the same as the previous OLS (0.61).

## 
## Call:
## lm(formula = regrs[[14]] ~ dat[, 1] + dat[, 2] + dat[, 3])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.4394 -1.6916 -0.5028  1.0860 16.2534 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.0904     0.2531  20.112   <2e-16 ***
## dat[, 1]      3.3447     0.3443   9.715   <2e-16 ***
## dat[, 2]      0.6351     0.3127   2.031   0.0443 *  
## dat[, 3]      0.3905     0.3147   1.241   0.2169    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.897 on 127 degrees of freedom
## Multiple R-squared:  0.6106, Adjusted R-squared:  0.6014 
## F-statistic: 66.39 on 3 and 127 DF,  p-value: < 2.2e-16

A cluster analysis was done to further study the featured census tracks. It shows clustering three would be appropriate.

## 
##  1  2  3 
## 55 32 44

## [1] 177.3648

Based on the 3 factors, 3 cluasters are presented in colors.

3 clusters were identified with the census track in Seattle.

Clustered census track

Each cluster shows unique features. Green groups comparatively have less housing stability and economic status while higher income inequality. Light blue groups are relatively opposite to the green groups. Light red groups keep their position in the middle of these 2 groups.

Residential solar installation is exactly showing the same pattern of the 1st factor (ML1), the housing stability in clustering.

It indicates that lower solar installation rate and lower total number of owner-occupied units with housing costs greater than $1000/month match the certified LIHTC census tracks (TRUE).

Hihger solar installation is correlated with higher housing unit median value. Cluster #3, #1 and #2 are in order of higher solar installation.

Time series analysis will help to understand the spatial-temporal pattern of residential solar installation in Seattle. Interestingly, one census track is noticably high in installation over the period.

Two different cumulative installation pattern and annual new installation pattern are mapped in each census track in Seattle. It shows cumulative number of installation is different from the annual new installation in that every year had different installation trend depending on census tracks. In addition, hotspot outlier analysis was performed for the annual new installation map.

Spatial-temporal installation in Seattle

The difference between cumulative number of installation hotspot and annual new installation hotspot shows the emerging area of increasing installation pattern in residential solar. It is noticable that West Seattle recenlty increases the installation while Ballad used to the one but goes slow these days. Columbia city presents both of cases that it has been and still maintaining the higher rate of installation. It's found that these areas are all clustered as light red (#1) and ligth blue (#3).

Hotspot for spatial-temporal cumulatative installation in Seattle

Hotspot for spatial-temporal annual installation in Seattle